%0 Journal Article
%D 2014
%T Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%K Gamma-convergence, Cahn-Hilliard functional, phase transitions
%X The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.
%I SISSA
%G en
%U http://hdl.handle.net/1963/7390
%1 7439
%2 Mathematics
%4 1
%# MAT/05 ANALISI MATEMATICA
%$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-06-19T16:24:43Z
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%0 Journal Article
%D 2013
%T Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%K singular nonlinear parabolic equations, Hilbert transform, thin films
%X In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6].
%I Springer
%G en
%U http://hdl.handle.net/1963/7245
%1 7284
%2 Mathematics
%4 1
%# MAT/05 ANALISI MATEMATICA
%$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-01-15T08:47:14Z
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%R 10.1007/s00205-014-0730-4
%0 Journal Article
%J Indiana Univ. Math. J. 60 (2011) 367-409
%D 2011
%T Singular perturbation models in phase transitions for second order materials
%A Milena Chermisi
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%X A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.
%B Indiana Univ. Math. J. 60 (2011) 367-409
%I Indiana University
%G en_US
%U http://hdl.handle.net/1963/3858
%1 851
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-27T10:47:12Z\\r\\nNo. of bitstreams: 1\\r\\nCheDMaFonLeo_2010.pdf: 350746 bytes, checksum: b384a4d0b82dd9713e1849ad3ef6a2be (MD5)
%R 10.1512/iumj.2011.60.4346
%0 Journal Article
%J Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331
%D 2010
%T Exact reconstruction of damaged color images using a total variation model
%A Irene Fonseca
%A Giovanni Leoni
%A Francesco Maggi
%A Massimiliano Morini
%X In this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.
%B Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/4039
%1 363
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-06T09:54:56Z\\nNo. of bitstreams: 1\\nflmm.pdf: 434739 bytes, checksum: f315d8807349e077c524fe14a1619a56 (MD5)
%R 10.1016/j.anihpc.2010.06.004
%0 Journal Article
%J Adv. Calc. Var. 3 (2010) 287-319
%D 2010
%T Nonlocal character of the reduced theory of thin films with higher order perturbations
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%B Adv. Calc. Var. 3 (2010) 287-319
%G en_US
%U http://hdl.handle.net/1963/3754
%1 563
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-15T09:06:42Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo.pdf: 288658 bytes, checksum: 7815e9376b53eb044b2fb2b57cd49b53 (MD5)
%R 10.1515/ACV.2010.012, /July/2010
%0 Journal Article
%J SIAM J. Math. Anal. 40 (2009) 2351-2391
%D 2009
%T A higher order model for image restoration: the one dimensional case
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%A Massimiliano Morini
%X The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.
%B SIAM J. Math. Anal. 40 (2009) 2351-2391
%G en_US
%U http://hdl.handle.net/1963/3174
%1 1127
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-23T07:52:52Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo-Mor-08-preprint.pdf: 336946 bytes, checksum: 32db893a2b928f559b6744296e1d4f2c (MD5)
%R 10.1137/070697823
%0 Journal Article
%J Arch. Ration. Mech. Anal. 186 (2007) 477-537
%D 2007
%T Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results
%A Irene Fonseca
%A Nicola Fusco
%A Giovanni Leoni
%A Massimiliano Morini
%X Strained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavorable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup in which the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume-constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero-contact-angle condition between islands and wetting layers.
%B Arch. Ration. Mech. Anal. 186 (2007) 477-537
%G en_US
%U http://hdl.handle.net/1963/2350
%1 1666
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-06T11:41:16Z\\nNo. of bitstreams: 1\\nwetting-december-30-06.pdf: 1519775 bytes, checksum: 40f435ddce013b1017d5c3e2369fa7c8 (MD5)
%R 10.1007/s00205-007-0082-4
%0 Journal Article
%J Arch. Rational Mech. Anal. 183 (2007) 411-456
%D 2007
%T Surfactants in Foam Stability: A Phase-Field Model
%A Irene Fonseca
%A Massimiliano Morini
%A Valeriy Slastikov
%X The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation.
%B Arch. Rational Mech. Anal. 183 (2007) 411-456
%G en_US
%U http://hdl.handle.net/1963/2035
%1 2161
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T15:51:40Z\\nNo. of bitstreams: 1\\n05-CNA-012.pdf: 414998 bytes, checksum: 3c44841388edba53080d531beadad798 (MD5)
%R 10.1007/s00205-006-0012-x
%0 Journal Article
%J Arch. Ration. Mech. Anal. 171 (2004) 55-81
%D 2004
%T Higher order quasiconvexity reduces to quasiconvexity
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%A Massimiliano Morini
%X In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems.
%B Arch. Ration. Mech. Anal. 171 (2004) 55-81
%I Springer
%G en_US
%U http://hdl.handle.net/1963/2911
%1 1789
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:36:19Z\\nNo. of bitstreams: 1\\nmath.AP0305138.pdf: 272082 bytes, checksum: 245f93702444ac3eb1de7c86c1f83551 (MD5)
%R 10.1007/s00205-003-0278-1